Dark energy, physical reality or illusion?

The standard model of cosmology, as opposed to the standard model of elementary particles, does not enjoy great generality: it is based on the simplest class of solutions among the solutions of Einstein's general relativity equations, that describe gravity and link matter distribution to the geometric properties of space-time. In particular, the basic assumption is that matter is approximated to a perfectly homogeneous fluid.

#LLL# Three-dimensional distribution of galaxiesfrom SDSS catalogue (http://www.sdss.org). Each point is a galaxy.The "butterfly"shape is due to the fact that the observations are made from the Earth towards the north and south galactic hemisphere. You can clearly identify the networkof structures, filaments and voids that formlarge scale galaxies in the universe. A homogeneous distribution would be characterized by the absence of structures and galaxies would be distributed in a perfectly uniform manner. (Source: Rien van de Weygaert, Erwin Platen arXiv:0912.2997v1)

Clearly, the properties of the real universe, characterized by large structures of galaxies and therefore by large fluctuations in mass (see picture), are not necessarily described by such a simplified idealization. The key point from the theoretical point of view is whether an non-homogeneous distribution of matter as the one observed in large-scale distribution of galaxies can be described, and how, in terms of spatial averages of Einstein's equations. That is, by averages calculated on large enough volumes as to safely assume that the fluctuations of matter are statistically the same in each volume. This question is now at the heart of a lively discussion in the cosmological literature for its important implications for the interpretation of data provided by observations.

In the standard cosmological model, in order to explain the observed data and make them compatible with theoretical predictions, it is necessary to assume the existence of two fundamental constituents whose origin and properties are completely unknown: dark matter and dark energy (or cosmological constant ). The latter is supposed to be a gravitationally repulsive form of energy making up three-quarters of the density of mass and energy of the universe. Dark matter instead is supposed to have properties that go beyond what is predicted by the standard model of elementary particles and should provide about a quarter of the density of mass-energy in the universe. In this scenario, ordinary baryonic matter (protons, neutrons, etc..) would provide only 5% of the density of the universe. However it is worth noting that the properties and the abundance of matter and dark energy are derived precisely from that 5% that we can observe in the form of light radiation. While direct evidence of the presence of non-baryonic matter and dark energy is very elusive, their primary role in cosmological models are precisely due to theoretical reasons that ultimately come from having solved Einstein's equations on the basis of the simplest possible assumptions. For this reason, in recent years we have witnessed a great development of theoretical research in the field of non-homogeneous models

This activity can be divided into two main strands. On the one hand there are attempts to use specific assumptions about the properties of the density field that generates the gravitational field. For example, it has been assumed that our galaxy is located near the center of a great void, whose effect is to distort the geometric properties of spacetime in such a way as to simulate the effect of dark energy. That is, in this scenario dark energy would result from the interpretation according to the standard models of a non-homogeneous yet spherically symmetric distribution of matter. This model has the "disadvantage" of introducing a "privileged" point , which is the center of the void. A post-Copernican cosmological theory however requires the equivalence of all observers and the absence of a privileged center or direction. However, one can generalize this model assuming that there are many voids and that our galaxy is "by chance" located at the center of one of them. In short, the solutions to Einstein's equations for an arbitrary distribution of matter are very difficult to find and you have to go with what you have, that is very strong simplifying assumptions. However, the standard model is just based upon the most simplifying assumptions!

The other strand, which was initiated and pursued with great determination by Thomas Buchert of the University of Lyon, has a different approach to the problem. On the one hand it preserves the Copernican principle according to which matter distribution is statistically homogeneous and isotropic, and therefore there are no privileged observers or directions. On the other hand, the assumption of a perfect spatial homogeneity of matter is relaxed, that is, it is admitted that there may be inhomogeneities in the distribution of mass, just as it is observed in the configuration of large scale galaxies in the universe. At this point, Einstein's equations are solved considering volume averages, on large enough volumes as to mediate the effect of inhomogeneities, and new equations are derived, that describe the average behaviour of space time properties and space-time evolution over time. The most striking result concerns the very fact that the fluctuations of matter give rise to an additional term (backreaction) if compared to the equations derived assuming a perfectly homogeneous fluid. In the equations, the term backreaction has the same role that the cosmological constant has in the standard models, and plays the same role from a dynamic point of view. Therefore, according to this model dark energy could be explained by the effect of matter fluctuations. Quantitative forecasts are yet to be produced, on the basis of which it would be possible to elaborate a sophisticated model like the standard model and research in this field is currently one of the frontiers of modern cosmology. However, the implications could be sensational not only for the understanding of dark energy but also in the interpretation of the various data provided by observations, including a reduction in the quantity and of the dynamic role of non-baryonic dark matter.

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